International Journal of Fuzzy Systems

, Volume 19, Issue 6, pp 1768–1781 | Cite as

State and Faults Estimation Based on Proportional Integral Sliding Mode Observer for Uncertain Takagi–Sugeno Fuzzy Systems and its Application to a Turbo-Reactor

  • Ilyes Elleuch
  • Atef Khedher
  • Kamel Ben Othman


This paper deals with the problem of state and faults estimation for nonlinear uncertain systems described by Takagi–Sugeno fuzzy structures (called also multiple models). In this work, actuator faults are considered as unknown inputs. The state and faults estimation is made using a structure of sliding mode observer where an integral term is added. This new structure of observer is called proportional integral sliding mode observer. The added integral term permits the unknown input estimation. For the sensor faults estimation, a mathematical transformation is used. The application of this mathematical transformation to the initial system output let to conceive an augmented system where the initial sensor fault appears as an unknown input. The observer convergence conditions are formulated in the form of Linear Matrix Inequalities allowing computing the observer gains. The proposed proportional integral sliding mode observer is applied to a numerical example showing the efficiency of the fault and the state estimation. In order to show the efficiency of the proposed method, it is applied to a turbo-reactor system.


Takagi–Sugeno fuzzy systems Proportional integral sliding mode observer Sensor faults Actuator faults State and faults estimation Unknown inputs 


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Ilyes Elleuch
    • 1
  • Atef Khedher
    • 2
  • Kamel Ben Othman
    • 3
  1. 1.LARATSI, ENIM, University of SousseSousseTunisia
  2. 2.LARA Automatic, ENITSousseTunisia
  3. 3.LARATSI, ENIMSousseTunisia

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